{"paper":{"title":"Hellings and Downs correlation of an arbitrary set of pulsars","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.CO","astro-ph.HE","astro-ph.IM"],"primary_cat":"gr-qc","authors_text":"Bruce Allen, Joseph D. Romano","submitted_at":"2022-08-15T14:40:29Z","abstract_excerpt":"Pulsar timing arrays (PTAs) detect gravitational waves (GWs) via the correlations they induce in the arrival times of pulses from different pulsars. We assume that the GWs are described by a Gaussian ensemble. The mean correlation $h^2 \\mu_{\\rm u}(\\gamma)$ as a function of the angle $\\gamma$ between the directions to two pulsars was predicted by Hellings and Downs (HD) in 1983. The variance $\\sigma^2_{\\rm tot}(\\gamma)$ in this correlation was recently calculated by Allen[11] for a single noise-free pulsar pair at angle $\\gamma$, which shows that after averaging over many pairs, the variance re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07230","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.07230/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}